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Optimization of the Superconducting Linear Magnetic Bearing of a Maglev Vehicle



Considering the need for cost/performance prediction and optimization of superconducting maglev vehicles, we develop and validate here a 3D finite element model to simulate superconducting linear magnetic bearings. Then we reduce the 3D model to a 2D model in order to decrease the computing time. This allows us to perform in a reasonable time a stochastic optimization considering the superconductor properties and the vehicle operation. We look for the permanent magnet guideway geometry that minimizes the cost and maximizes the lateral force during a displacement sequence, with a constraint on the minimum levitation force. The displacement sequence reproduces a regular maglev vehicle operation with both vertical and lateral movements. For the sake of comparison, our reference is the SupraTrans prototype bearing. The results of the optimization suggest that the bearing cost could be substantially reduced, while keeping the same performances as the initial design. Alternatively, the performances could be significantly improved for the same original cost.
4014 12
PM guideway I
PM guideway C
PM guideway B
2714 18
PM guideway A
Optimization of the Superconducting Linear
Magnetic Bearing of a Maglev Vehicle
Loïc Quéval
, Guilherme G. Sotelo
, Y. Kharmiz
, Daniel H.N. Dias
, Felipe Sass
1 Lab for Electrical Machines, University of Applied Sciences, Düsseldorf, Germany.
2 Fluminense Federal University, Niterói (RJ), Brazil.
3 Karlsruhe Institute of Technology, Eggenstein-Leopoldshafen, Germany.
Develop and validate a 3D FE model of a superconducting linear magnetic bearing.
Reduce the 3D model to a 2D model to decrease the computing time while keeping a good accuracy.
Use the 2D model to optimize the bearing cost considering a displacement sequence.
PM guideway model
We developed a superconducting linear magnetic bearing 3D finite element model. It is
based on the H-formulation with a power law E-J relationship. The J
(B) dependence, the PM
guideway real geometry and the iron nonlinearity are included. The model is validated by
comparison with experimental data. For the optimization, the 3D model is reduced to a 2D
model by shortening artificially its length, instead of decreasing the critical current density.
Taking the SupraTrans prototype bearing as reference, the PM guideway optimization results
show that it is possible to greatly reduce the cost for the same performances on a given
displacement sequence; or to greatly improve the performances for the same cost.
Víctor M.R. Zermeno
, Raimund Gottkehaskamp
ID: 3A-LS-P-04.03
From 3D to 2D
It is common practice to calibrate the critical current density J
of the bulk using the
maximum levitation force measured during the ZFC sequence.
We consider the bearing initially designed and optimized for the SupraTrans maglev vehicle
HTS bulk model
SLMB model
(a) Zero field cooling
(b) Vertical displacement downward
(c) Vertical displacement upward.
(a) Field cooling
(b) Vertical displacement downward
(c) Lateral displacements.
What: Permanent magnets and iron pieces
arranged in flux concentrator.
How: 2D magnetostatic FEM
- iron nonlinear BH curve
- real geometry.
What: 3-seeded melt-textured YBCO block.
How: 2D or 3D H-formulation FEM
- power law E-J relationship
- isotropic Kim like model Jc(B)
- 3 independent domains.
How: Unidirectional coupling between HTS bulk
model and PM guideway model.
- only 1 static solution of the PM guideway model
- reduced LN
domain around HTS bulk.
Objective and constraints
3D model 2D model
with reduced J
with reduced d
2D model
Dimensions of PM guideway : 4 parameters
Dimensions of HTS bulk : unchanged
Computing time < 1 min
We look for the PM guideways that minimize the cost of the guideway and maximize the
lateral force during LD sequence, with a constraint on the minimum levitation force,
Multi-objective Particule Swarm Optimization (PSO)
- 100 particules
- 25 generations
Total computing time ~40 h
Optimization algorithm
Fig. 1 - SLMB Geometry.
Fig. 2 - Magnetic flux density above the PM guideway
at z = 1, 5, 10, 20 mm.
Fig. 3 - Levitation force for ZFC sequence.
Fig. 4 - Lateral force for LD sequence.
Fig. 5 - Levitation force for LD sequence.
Note: The decrease of the levitation force during lateral displacements should be taken into
account during the optimization.
"Optimization on a displacement sequence"
5 mm
ZFC sequence
LD sequence
5 mm
25 mm 100 mm
10 mm
Fig. 8 - Initial and optimized PM guideways.
Dimensions in mm (on scale).
where , , .
cost [€/m]
PM guideway I
PM guideway A
PM guideway B
PM guideway C
-23 %
+38 %
Fig. 7 - Bi-objective optimization results.
Fig. 6 - Parametrization of the PM guideway.
ac d
... N UMERICAL simulation of the HTS magnetic levitation (maglev) system is fundamental to various practical applications [1]- [3]. At present, the numerical researches of HTS maglev are mostly focusing on the cases with permanent magnetic fields [1]- [6]. ...
... N UMERICAL simulation of the HTS magnetic levitation (maglev) system is fundamental to various practical applications [1]- [3]. At present, the numerical researches of HTS maglev are mostly focusing on the cases with permanent magnetic fields [1]- [6]. Limited by the available magnetization of permanent magnet, the effective magnetic field in the current HTS maglev system is generally around 0.5 T [7], [8]. ...
In this paper, high magnetic fields generated by HTS magnet instead of permanent magnet was adopted to en-hance the levitation property of HTS bulk on the fact that levita-tion force is positively related to the magnetic field strength. Based on the generally-accepted H-formulation, a validated 2-D axisymmetric finite element model was established to study and predict the levitation performances of HTS bulk in high magnetic fields. The fishtail effect $J_c(\vert B\vert,T)$ dependence, which is closer to reality demonstrating unique magnetic dependence of HTS criti-cal current in high magnetic fields, was employed to improve the effectiveness of numerical model. The results indicate that the levitation force could be greatly improved by taking magnetic field close to the peak field of fishtail effect $J_c(\vert B\vert,T)$ curve. This work could serve as a vital method to predict the levitation per-formance of HTS bulk in high magnetic fields and a guide con-cerning how to choose external filed in balance of performance and cost in future applications.
... Work on optimizing the superconducting linear magnetic bearing of a maglev vehicle was presented [5]. A multiobjective multi-constraint optimization to minimize the cost or volume of the 3D bearing geometry, considering variable component dimensions and spacing, was initially performed in [6]. ...
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This document presents a study on the optimization of the 3D geometry of a horizontal axis radial levitation bearing with zero-field cooled (ZFC) high-temperature superconductor (HTS) bulks in the stator, and radially magnetized permanent magnet (PM) rings in the rotor. The optimization of component dimensions and spacing to minimize the volume or cost concerning only the maximization of the levitation force was previously studied. The guidance force and guiding stability depend on the spacing between PM rings in the rotor and between the rings of HTS bulks in the stator. This new optimization study aims to find the optimum spacing that maximize the guidance force with given HTS bulk and PM ring dimensions while maintaining the minimum required levitation force. Decisions are taken using the non-dominated sorting genetic algorithm (NSGA-II) over 3D finite element analysis (FEA). A simplified electromagnetic model of equivalent relative permeability is used on 3D FEA to reduce numerical processing and optimization time. Experimental prototypes were built to measure magnetic forces and validate appropriate values of equivalent magnetic permeability. An analysis of stable and unstable geometry domains depending on the spacing between rings of HTS bulks and PM rings is also done for two HTS bulk sizes.
High-temperature superconducting (HTS) bulks in HTS Maglev systems are always arrayed in a combination to make full use of the applied magnetic field of the permanent magnet guideway (PMG). An excellent combination scheme improves the overall levitation and guidance performance significantly. In this paper, a three-dimensional (3D) electromagnetic model of the real HTS-PMG maglev system with an HTS bulk array was established. This model comprehensively expresses the influence of various factors on the E – J relationship and the 3D spatial distribution of J c , including internal factors such as the inhomogeneity and anisotropy of electromagnetic characteristics, as well as external factors such as applied magnetic field and working temperature. A ternary function was proposed to describe the uneven distribution of J c caused by the bulk’s growth process, which is an interesting phenomenological modeling attempt. In the simulations of the bulks’ combinations, perfect magnetic conductor boundary conditions were applied on the contact surface to simulate two bulks touching each other. Besides, the research target includes reproducing the shapes, the orientations, and the combination scheme of HTS bulks in the real PMG magnetic field. The calculation results of levitation force of the cylindrical bulk under different spatial orientations above the PMG were compared with the experimental results, through which the accuracy of the model was verified. On this basis, the influence of the magnetic field generated by the superconducting current on the nearby bulk was further explored. It was found that this magnetic field has a small contribution to the total levitation force and a relatively obvious influence on the guidance force. When the lateral displacement is large, such as 5 mm, the magnetic field generated by the superconducting current slightly increases the total guidance force stiffness. According to more simulated conditions, some optimization strategies on bulk combinations were proposed. This work provides not only a 3D descriptive model for fitting the real multi-bulk-combination maglev scenarios but also some optimization strategies for the HTS maglev transportation applications.
An overview of experimental and theoretical studies of the characteristics of maglev systems using high-temperature superconductors (HTSC) is presented. Materials used in maglev technologies, namely bulk superconductors and HTSC tape composites, are considered. The main experimental data obtained on both bulk and tape superconductors assembled in stacks of various configurations are demonstrated. The factors influencing the magneto-force characteristics are analyzed: geometric parameters, the influence of external alternating magnetic fields, temperatures, relaxation phenomena. A significant part of the review is devoted to the description of various methods for calculating maglev systems, including those based on stacks of HTSC composites. The features of thermal processes in maglev systems with cryocooler and nitrogen cooling are considered. General recommendations for the creation of optimal maglev systems based on tape HTSC composites are given.
For high-temperature superconducting (HTS) maglev, an electromagnet guideway unit (EMGU) that can form an electromagnet guideway (EMG) with a small gap, or even no gap, between EMGUs has been designed. The longitudinal magnetic fields along a single EMGU and two EMGUs arranged in a line were first investigated through measurement and simulation. The experimentally measured data validated the simulation results from a three-dimensional (3D) EMGU model implemented in COMSOL Multiphysics, indicating that the model is reliable and can be used for further studies. The dynamic responses of a high-temperature superconducting (HTS) bulk above a single EMGU and two EMGUs arranged in a line, including the dynamic levitation force (LF) and traveling directional force (TDF), under different operating conditions were investigated through experiment and simulation using a segregated H -formulation model. The magnetic field and current density distributions inside the superconductor are affected by the external magnetic field generated by the EMGU and are responsible for the dynamic characteristics. Finally, the segmented instant excitation (SIE) mode was investigated through simulation, which shows it is feasible by coordinating the currents of EMGUs.
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High-temperature superconducting (HTS) maglev, owing to its unique self-stability characteristic, has a wide range of application prospect in flywheel energy storage, magnetic levitation bearing, rail transportation, and other fields. As the important foundation of the engineering application, researches on the dynamic characteristics of HTS maglev have attracted more and more attention. As most of existing models adopted the power exponential function to approximately fit the relationship between the force and displacement, which can only qualitatively analyze the dynamic characteristics of HTS maglev, this paper employs the flux flow and creep model to deduce a 2D H formulation of the HTS maglev system to make up for this deficiency. Moreover, related experiments were also carried out to validate the accuracy of this simulation model and comparisons with other previous models have been achieved. The results prove that the simulation model can reduce the calculation time still with a good convergence. Then, an electromagnetic-thermal-force multiphysics coupling model was established to analyze the dynamic characteristics, especially the levitation height drift of an HTS bulk above the permanent magnet guideway. Results indicate that when the superconductor has an initial velocity that causes disturbance at the working position, vibration and drift phenomena will occur, and the vertical levitation drift also grows as the velocity increases. The simulation results also show that resonance will occur if the excitation frequency is close to the HTS maglev system’s resonance frequency, and a strong “beat” phenomenon will occur if the excitation frequency is close to twice the main vibration frequency of the system. Additionally, the HTS maglev system shows good anti-vibration ability on the relatively low-frequency region as well as the high-frequency region, which proves that it can be well applied to the rail transportation field. All results could be supported as references for the design of HTS maglev systems and its future application.
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An electromagnet guideway unit (EMGU) that can form an electromagnet guideway (EMG) with only a small gap, or even no gap, between multiple EMGUs was designed. The magnetic characteristics of such EMGU(s), including the homogeneity of the magnetic field along the EMGU(s) and the transverse magnetic field distribution were first investigated. As expected, the EMGU(s) can provide a homogeneous magnetic field in order to levitate bulk superconductors. Simulation results from an EMGU model implemented in COMSOL Multiphysics were verified using experimentally measured data, which indicated the established model can be used for further study and analysis. Next, the levitation characteristics of a high-temperature superconducting (HTS) bulk above the EMGU, including the levitation force acting on HTS bulk due to its interaction with the EMGU, as well as the stability of the bulk when experiencing a lateral disturbance and when varying the current of the EMGU, were investigated through experiment and simulation. The behavior of the levitation force during re-magnetization of the EMGU indicated that a larger re-magnetizing current is needed to suppress the internal magnetic field (trapped field) obtained from the pre-magnetization process, thereby providing a repulsive force to the superconductor. The stability study showed that the HTS maglev system with an EMGU with adjustable current can not only deal with a reduction of the levitation force but can also increase the restoring force when the superconductor is disturbed laterally. Finally, in order to clarify the mechanism of these levitation characteristics, the internal electromagnetic characteristics of the HTS bulk were analyzed using a 2D model.
In the design of maglev systems, the levitation force determines the levitation height and the dynamic stability associated with potential vibrations, especially the offset of the levitation point relative to the working point. However, such two key parameters are often antagonistic: a relatively low dynamic stability comes with a high levitation force, whereas a relatively low levitation force can come with a high dynamic stability. In this paper, we will discuss several strategies to deal with this problem by means of a two-dimensional numerical model based on Newton's second law and Maxwell's equations together with a power-law constitutive relation. The dynamics of maglev systems consisting of a bulk high-temperature superconductor and a Halbach-type permanent-magnet guideway with soft ferromagnets are analyzed. The results show that the drift phenomenon occurs in both vertical and lateral directions triggered by a transverse disturbance, and preloading can alleviate such a phenomenon, but this will lead to a reduction in the levitation force. Improved preloading is effective in enhancing the levitation force without sacrificing the dynamic stability. In some systems, the levitation force and dynamic stability can be further improved by adjusting the soft ferromagnets to an appropriate location in the guideway. Moreover, some guidelines on how the superconducting part should be designed are provided in order to overcome the technical difficulty and reduce the material consumption while at the same time maintaining the dynamic levitation performance.
In order to decouple the three-degree-of-freedom six-pole active magnetic bearing (3-DOF 6-pole AMB) with strong couplings, nonlinear and unstable disturbance, an active disturbance rejection control strategy based on BP neural network (ADRC-BP) is put forward. Firstly, the configuration, magnetic circuit, working principle and mathematical model of 3-DOF 6-pole AMB are introduced and established. Then, taking the 3-DOF 6-pole AMB as the controlled object, an ADRC-BP system is designed and a method of parameter tuning is proposed. Finally, the effectiveness of the control strategy is verified by simulation and experiments. The results show that the ADRC-BP has strong robustness and adaptability to the uncertainty of magnetic bearing model and the variation of external disturbance. The decoupling control effect of ADRC-BP is better than that of conventional ADRC.
The linear superconducting magnetic bearing (SMB) discussed in this paper consists of a high temperature superconducting (HTS) bulk of YBaCuO and a permanent magnet (PM) rail to provide the excitation magnetic field. The dynamics of SMB is vital to engineering applications, however, previous experimental and theoretical explorations on dynamic behaviors of linear SMB only provide qualitative analysis, because of limited experimental conditions and approximated analytical models. Furthermore, the pulsed and harmonic excitations have not been taken into account in the published numerical works on the dynamics of linear SMB. In this paper, a 2-dimensional (2-D) model of the linear SMB was introduced and coupled with the 2-D motion $2^{\text{nd}}$ -order equations with respect to time, to simulate the dynamic behaviors in the vertical and lateral directions. Under the external excitations, the displacements in time and frequency domains, phase trajectories, and motion trajectories are presented in the vertical and lateral directions to discuss the effects of pulsed and harmonic forces on the dynamic characteristics of linear SMB. It turns out that the 2-D model with ease of implementation can provide a utile tool for analyzing the dynamics of linear SMB, and the numerical results, inaccessible through simplified analytical models, provide the quantitative dynamic characteristics and principles for applications of linear SMB.
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The use of superconducting magnetic bearings in transportations promises an increase of energy efficiency. A maglev vehicle is being developed at Federal University of Rio de Janeiro based on the levitation between superconductors and permanent magnets. It is an opportunity to evaluate the operational costs of a superconducting magnetic bearing in a real large scale application. On the other hand, big projects are born from small experiments and lots of simulation results. Specifically for the magnetic bearing applica-tion there are some simulation methods available in the literature, each one with its own limitations and its own difficulties inherent to the implementation. The goal of this work is to study an easy way to implement a magnetic bearing simulation using a commercial finite element software to solve a H-formulation model. The superconductor behavior is described by the Power-Law's E-J relationship and simulated levitation force results are compared to experimental measurements.
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The superconducting MagLev technology for transportation systems is becoming mature due to the research and developing effort of recent years. The Brazilian project, named MagLev-Cobra, started in 1998. It has the goal of developing a superconducting levitation vehicle for urban areas. The adopted levitation technology is based on the diamagnetic and the flux pinning properties of YBa2Cu3O7−δ (YBCO) bulk blocks in the interaction with Nd-Fe-B permanent magnets. A laboratory test facility with permanent magnet guideway, linear induction motor and one vehicle module is been built to investigate its operation. The MagLev-Cobra project state of the art is presented in the present paper, describing some construction details of the new test line with 200 m.
Magnetized YBaCuO bulks are available to enhance the levitation performance of present superconducting maglev systems due to their high trapped fields. To realize a good YBaCuO bulk magnet, we studied the flux-trapping properties of an YBaCuO bulk sample under different magnetization fields from two aspects. Firstly in spatial view, five Hall sensors were employed to measure the trapped magnetic fields at five typical positions of growth sector regions and growth sector boundaries on the seeded surface of the bulk. And then in temporal view, the trapped magnetic fields of these five positions were continually recorded by a real-time data acquisition device during the magnetization process and the succeeding relaxation processes. Results show that the saturated trapped fields at five surface positions of the YBaCuO bulk magnet exhibit the strong spatial inhomogeneity. The trapped fields at the growth sector boundaries are always higher than those at the growth sector regions, due to different critical current density distributions of the bulk superconductor. And the magnetization field required to saturate the center of the bulk is much higher than that of the edge region. But the much high magnetization field will reduce the final trapped field at the edge of the bulk. Moreover the trapped field variation with time is sensitive to the participation of some external ferromagnetism materials. It is found that the adding of an iron plate above the YBaCuO bulk surface is efficacious to restrain the trapped field relaxation.
Superconducting coated conductors have been used for several large-scale applications. One potential application for YBCO second-generation (2G) wire is the development of superconducting magnetic bearings (SMB). The main advantages of 2G wires are large scale production, high critical current density values, lower manufacturing cost than first generation, and superior performance under high magnetic fields. This work proposes a study of a linear SMB using 2G wires as a passive levitator for MagLev vehicles. The 2G block is conceived to replace the YBCO bulk in the MagLev's SMB prototype, which is being built at Federal University of Rio de Janeiro. In this context, a superconducting block using stacked 2G wires was built to evaluate the behavior of this SMB. The forces between the 2G block and a permanent magnet were measured and compared with the results for an YBCO bulk with nearly the same dimensions. The experimental rig used for this work allows vertical and lateral displacements and a load cell is used to evaluate the SMB levitation force decay due to the lateral movement. The 2G block has presented lower force levels than ordinary YBCO bulks, but it presents potential to be applied in a SMB application.
A robust and fast numerical course for investigating the magnetic levitation (maglev) performance of high-temperature superconductors (HTSs) is proposed and implemented via finite-element methods (FEMs) in this paper. This numerical course uses the magnetic vector potential as the state variable to establish the partial differential equations (PDEs) for governing the electromagnetic properties of 2-D simplified HTSs, a smoothed Bean-Kim's model of a critical state to describe the nonlinear constitutive law of HTSs, and the advanced algorithm of Jacobian-free Newton-Krylov (JFNK) to handle the nonlinear system of the FEM equation. After being tested, this homemade FEM model was applied to investigate the influence of various FEM parameters, e.g., the dimension of the computational domain, the prescribed tolerance for convergence, the coarseness of the mesh, and the time step, upon the precision of levitation/guidance force on an HTS bulk while moving in a nonuniform field generated by a permanent-magnet track. The most important findings through these studies are that the coarse choice of tolerance can cause the nonphysical phenomena such as the crossings in the force loops, and the numerical results are very robust against the dimension of the computational domain, the coarseness of the mesh, and the time step. Based on these findings, it was found that the time consumed for performing a typical cycle of levitation force calculation is merely a few seconds, making the application of this FEM model for optimizing the HTS maglev system very attractive.
The strongly connected or coupled grain boundaries (GBs) between adjacent grains and their macroembodiment as flowing intergrain supercurrents crossing the GBs inside multiseeded bulk high-temperature superconductors were elucidated by trapped-flux evaluation. Trapped-field measurements, after cutting and polishing two multiseeded YBCO bulk samples, were conducted to present the existence of coupled GBs and their distribution along the $c$-axis growth. The intensive trapped-flux density observed near the GB areas inside the whole sample is direct evidence of a strongly connected or coupled GB. The relatively strong trapped flux near the GB areas and the significant improvement of the total trapped flux compared with the isolated single-grain bulks were ascribed to the intergrain supercurrent flowing across the GBs in large macroscopic loops with coordination of the intragrain supercurrent circulating in each grain of the multiseeded bulk. Based on the experimental results, a simplified simulation model that incorporates two forms of the intra- and intersupercurrents flowing inside the multiseeded bulk is introduced to reproduce the trapped-flux density features, and qualitative agreement is obtained by comparison with the experimental ones.
Persistent currents induced in hard superconductors (HSC) were ; investigated by measuring the resulting magnetic effects. The tubular HSC ; examined were Nb powder, NbâSn, and 3Nb- Zr samples of uniform wall ; thickness and length large compared to the diameter. Experimental evidence is ; presented that in HSC the Lorentz force plays a crucial role in determining the ; critical current density and the critical persistent currents in decay with a ; measurable rate. (H.D.R.);
There is an intense research in maglev technology for providing convenient and safe transportation. In particular, sev- eral projects are being carried out worldwide -particularly in Ger- many, Brazil, and China- for constructing full-scale maglev trains. They are based on the levitation of superconducting pellets over magneticguideways.Theoptimizationof theirgeometricalparam- eters and the properties of both superconducting and magnetic parts become very important. Theoretical simulations capturing the essential physics of the superconducting levitation become a very useful tool for understanding and improving the devices. In this work, we extend previous numerical models to incorporate new features in order to simulate closer to actual maglev designs. Inparticular,weanalysehowthelevitationandguidanceforcesare modified when the superconducting part is composed of several su- perconductors as compared with a single one.
Finite-element models are a powerful and widely used tool for evaluating the ac losses of HTS tapes and wires as well as of assemblies such as cables and coils. The H-formulation, which uses the magnetic field components as state variables, has proved to be an efficient implementation to solve 2-D problems, involving infinitely long or axially-symmetric geometries; an excellent agreement with experimental data has been found in many cases. However, the simulation of certain applications requires a full 3-D model. In this paper we report on the development of a 3-D model based on the H-formulation. We describe the implementation of Maxwell equations, the imposition of current constraints and we discuss the issues related to meshing 3-D volumes. The model is validated by comparing the results with those obtained with 2-D models in cases that can be investigated in 2-D; then, it is used to simulate cases that can be handled only in 3-D.
High temperature superconductor Roebel cables are well known for their large current capacity and low AC losses. For this reason they have become attractive candidates for many power applications. The continuous transposition of their strands reduces the coupling losses while ensuring better current sharing among them. However, since Roebel cables have a true 3D structure and are made of several high aspect ratio coated conductors, modelling and simulation of their electromagnetic properties is very challenging. Therefore, a realistic model taking into account the actual layout of the cable is unavoidably a large scale computational problem. In this work, we present a full 3D model of a Roebel cable with 14 strands. The model is based on the H-formulation, widely used for 2D problems. In order to keep the 3D features of the cable (in particular the magnetization currents near the transpositions), no simplifications are made other than the reduction of the modelled length according to the periodicity of the cable structure. The 3D model is used to study the dependence of AC losses on the amplitude of the AC applied magnetic field or transport current. Beyond the importance of simulating the Roebel cable layout, this work represents a further step into achieving 3D simulation of superconducting devices for real applications.